// The contents of this file are in the public domain. See LICENSE_FOR_EXAMPLE_PROGRAMS.txt
/*
This is an example illustrating the use of the support vector machine
utilities from the dlib C++ Library.
This example creates a simple set of data to train on and then shows
you how to use the cross validation and svm training functions
to find a good decision function that can classify examples in our
data set.
The data used in this example will be 2 dimensional data and will
come from a distribution where points with a distance less than 10
from the origin are labeled +1 and all other points are labeled
as -1.
*/#include<iostream>#include<dlib/svm.h>usingnamespace std;
usingnamespace dlib;
intmain(){// The svm functions use column vectors to contain a lot of the data on which they
// operate. So the first thing we do here is declare a convenient typedef.
// This typedef declares a matrix with 2 rows and 1 column. It will be the object that
// contains each of our 2 dimensional samples. (Note that if you wanted more than 2
// features in this vector you can simply change the 2 to something else. Or if you
// don't know how many features you want until runtime then you can put a 0 here and
// use the matrix.set_size() member function)
typedef matrix<double, 2, 1> sample_type;
// This is a typedef for the type of kernel we are going to use in this example. In
// this case I have selected the radial basis kernel that can operate on our 2D
// sample_type objects
typedef radial_basis_kernel<sample_type> kernel_type;
// Now we make objects to contain our samples and their respective labels.
std::vector<sample_type> samples;
std::vector<double> labels;
// Now let's put some data into our samples and labels objects. We do this by looping
// over a bunch of points and labeling them according to their distance from the
// origin.
for(int r =-20; r <=20; ++r){for(int c =-20; c <=20; ++c){
sample_type samp;
samp(0)= r;
samp(1)= c;
samples.push_back(samp);
// if this point is less than 10 from the origin
if(sqrt((double)r*r + c*c)<=10)
labels.push_back(+1);
else
labels.push_back(-1);
}}// Here we normalize all the samples by subtracting their mean and dividing by their
// standard deviation. This is generally a good idea since it often heads off
// numerical stability problems and also prevents one large feature from smothering
// others. Doing this doesn't matter much in this example so I'm just doing this here
// so you can see an easy way to accomplish this with the library.
vector_normalizer<sample_type> normalizer;
// let the normalizer learn the mean and standard deviation of the samples
normalizer.train(samples);
// now normalize each sample
for(unsignedlong i =0; i < samples.size(); ++i)
samples[i] =normalizer(samples[i]);
// Now that we have some data we want to train on it. However, there are two
// parameters to the training. These are the nu and gamma parameters. Our choice for
// these parameters will influence how good the resulting decision function is. To
// test how good a particular choice of these parameters is we can use the
// cross_validate_trainer() function to perform n-fold cross validation on our training
// data. However, there is a problem with the way we have sampled our distribution
// above. The problem is that there is a definite ordering to the samples. That is,
// the first half of the samples look like they are from a different distribution than
// the second half. This would screw up the cross validation process but we can fix it
// by randomizing the order of the samples with the following function call.
randomize_samples(samples, labels);
// The nu parameter has a maximum value that is dependent on the ratio of the +1 to -1
// labels in the training data. This function finds that value.
constdouble max_nu =maximum_nu(labels);
// here we make an instance of the svm_nu_trainer object that uses our kernel type.
svm_nu_trainer<kernel_type> trainer;
// Now we loop over some different nu and gamma values to see how good they are. Note
// that this is a very simple way to try out a few possible parameter choices. You
// should look at the model_selection_ex.cpp program for examples of more sophisticated
// strategies for determining good parameter choices.
cout << "doing cross validation" << endl;
for(double gamma =0.00001; gamma <=1; gamma *=5){for(double nu =0.00001; nu < max_nu; nu *=5){// tell the trainer the parameters we want to use
trainer.set_kernel(kernel_type(gamma));
trainer.set_nu(nu);
cout << "gamma: " << gamma << " nu: " << nu;
// Print out the cross validation accuracy for 3-fold cross validation using
// the current gamma and nu. cross_validate_trainer() returns a row vector.
// The first element of the vector is the fraction of +1 training examples
// correctly classified and the second number is the fraction of -1 training
// examples correctly classified.
cout << " cross validation accuracy: " <<cross_validate_trainer(trainer, samples, labels, 3);
}}// From looking at the output of the above loop it turns out that a good value for nu
// and gamma for this problem is 0.15625 for both. So that is what we will use.
// Now we train on the full set of data and obtain the resulting decision function. We
// use the value of 0.15625 for nu and gamma. The decision function will return values
// >= 0 for samples it predicts are in the +1 class and numbers < 0 for samples it
// predicts to be in the -1 class.
trainer.set_kernel(kernel_type(0.15625));
trainer.set_nu(0.15625);
typedef decision_function<kernel_type> dec_funct_type;
typedef normalized_function<dec_funct_type> funct_type;
// Here we are making an instance of the normalized_function object. This object
// provides a convenient way to store the vector normalization information along with
// the decision function we are going to learn.
funct_type learned_function;
learned_function.normalizer = normalizer; // save normalization information
learned_function.function = trainer.train(samples, labels); // perform the actual SVM training and save the results
// print out the number of support vectors in the resulting decision function
cout << "\nnumber of support vectors in our learned_function is "
<< learned_function.function.basis_vectors.size()<< endl;
// Now let's try this decision_function on some samples we haven't seen before.
sample_type sample;
sample(0)=3.123;
sample(1)=2;
cout << "This is a +1 class example, the classifier output is " <<learned_function(sample)<< endl;
sample(0)=3.123;
sample(1)=9.3545;
cout << "This is a +1 class example, the classifier output is " <<learned_function(sample)<< endl;
sample(0)=13.123;
sample(1)=9.3545;
cout << "This is a -1 class example, the classifier output is " <<learned_function(sample)<< endl;
sample(0)=13.123;
sample(1)=0;
cout << "This is a -1 class example, the classifier output is " <<learned_function(sample)<< endl;
// We can also train a decision function that reports a well conditioned probability
// instead of just a number > 0 for the +1 class and < 0 for the -1 class. An example
// of doing that follows:
typedef probabilistic_decision_function<kernel_type> probabilistic_funct_type;
typedef normalized_function<probabilistic_funct_type> pfunct_type;
pfunct_type learned_pfunct;
learned_pfunct.normalizer = normalizer;
learned_pfunct.function =train_probabilistic_decision_function(trainer, samples, labels, 3);
// Now we have a function that returns the probability that a given sample is of the +1 class.
// print out the number of support vectors in the resulting decision function.
// (it should be the same as in the one above)
cout << "\nnumber of support vectors in our learned_pfunct is "
<< learned_pfunct.function.decision_funct.basis_vectors.size()<< endl;
sample(0)=3.123;
sample(1)=2;
cout << "This +1 class example should have high probability. Its probability is: "
<<learned_pfunct(sample)<< endl;
sample(0)=3.123;
sample(1)=9.3545;
cout << "This +1 class example should have high probability. Its probability is: "
<<learned_pfunct(sample)<< endl;
sample(0)=13.123;
sample(1)=9.3545;
cout << "This -1 class example should have low probability. Its probability is: "
<<learned_pfunct(sample)<< endl;
sample(0)=13.123;
sample(1)=0;
cout << "This -1 class example should have low probability. Its probability is: "
<<learned_pfunct(sample)<< endl;
// Another thing that is worth knowing is that just about everything in dlib is
// serializable. So for example, you can save the learned_pfunct object to disk and
// recall it later like so:
serialize("saved_function.dat")<< learned_pfunct;
// Now let's open that file back up and load the function object it contains.
deserialize("saved_function.dat")>> learned_pfunct;
// Note that there is also an example program that comes with dlib called the
// file_to_code_ex.cpp example. It is a simple program that takes a file and outputs a
// piece of C++ code that is able to fully reproduce the file's contents in the form of
// a std::string object. So you can use that along with the std::istringstream to save
// learned decision functions inside your actual C++ code files if you want.
// Lastly, note that the decision functions we trained above involved well over 200
// basis vectors. Support vector machines in general tend to find decision functions
// that involve a lot of basis vectors. This is significant because the more basis
// vectors in a decision function, the longer it takes to classify new examples. So
// dlib provides the ability to find an approximation to the normal output of a trainer
// using fewer basis vectors.
// Here we determine the cross validation accuracy when we approximate the output using
// only 10 basis vectors. To do this we use the reduced2() function. It takes a
// trainer object and the number of basis vectors to use and returns a new trainer
// object that applies the necessary post processing during the creation of decision
// function objects.
cout << "\ncross validation accuracy with only 10 support vectors: "
<<cross_validate_trainer(reduced2(trainer,10), samples, labels, 3);
// Let's print out the original cross validation score too for comparison.
cout << "cross validation accuracy with all the original support vectors: "
<<cross_validate_trainer(trainer, samples, labels, 3);
// When you run this program you should see that, for this problem, you can reduce the
// number of basis vectors down to 10 without hurting the cross validation accuracy.
// To get the reduced decision function out we would just do this:
learned_function.function =reduced2(trainer,10).train(samples, labels);
// And similarly for the probabilistic_decision_function:
learned_pfunct.function =train_probabilistic_decision_function(reduced2(trainer,10), samples, labels, 3);
}